Final answer:
To find the interest earned on a $4,000 investment with a 15% annual interest rate compounded annually over 2 years, we use the compound interest formula. The total amount after 2 years is $5,290, therefore the interest earned is $1,290.
Step-by-step explanation:
To calculate the interest earned on Debbie's account over 2 years with a 15% interest rate compounded annually, we can use the compound interest formula:
A = P (1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal form).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested or borrowed for, in years.
Given that P is $4,000, r is 15% or 0.15, n is 1 (since it is compounded annually), and t is 2 years, the calculation is:
A = $4,000 (1 + 0.15/1)^(1*2)
A = $4,000 (1.15)^2
A = $4,000 * 1.3225
A = $5,290
So, the total amount in Debbie's account after 2 years would be $5,290. The interest earned is:
Interest Earned = Total Amount - Principal
Interest Earned = $5,290 - $4,000
Interest Earned = $1,290
Therefore, to the nearest cent, Debbie will earn $1,290 in interest over 2 years.